A Mathematical Model for Human Intelligence

Curiosity and Intelligence

People have been trying to figure out what intelligence is, and how it differs from person to person, for centuries. Much has been written on the subject, and some of this work has helped people. Unfortunately, much harm has been done as well. Consider, for example, the harm that has been done by those who have had such work tainted by racism, sexism, or some other form of “us and them” thinking. This model is an attempt to eliminate such extraneous factors, and focus on the essence of intelligence. It is necessary to start, therefore, with a clean slate (to the extent possible), and then try to figure out how intelligence works, which must begin with an analysis of what it is.

If two people have the same age — five years old, say — and a battery of tests have been thrown at them to see how much they know (the amount of knowledge at that age), on a wide variety of subjects, person A (represented by the blue curve) may be found to know more, at that age, than person B (represented by the red curve). At that age, one could argue that person A is smarter than person B. Young ages are found on the left side of the graph above, and the two people get older, over their lifespans, as the curves move toward the right side of the graph.

What causes person A to know more than person B, at that age? There can be numerous factors in play, but few will be determined by any conscious choices these two people made over their first five years of life. Person B, for example, might have been affected by toxic substances in utero, while person A had no such disadvantage. On the other hand, person A might simply have been encouraged by his or her parents to learn things, while person B suffered from parental neglect. At age five, schools are not yet likely to have had as much of an impact as other factors.

An important part of this model is the recognition that people change over time. Our circumstances change. Illnesses may come and go. Families move. Wars happen. Suppose that, during the next year, person B is lucky enough to get to enroll in a high-quality school, some distance from the area where these two people live. Person B, simply because he or she is human, does possess curiosity, and curiosity is the key to this model. Despite person B‘s slow start with learning, being in an environment where learning is encouraged works. This person begins to acquire knowledge at a faster rate. On the graph, this is represented by the red curve’s slope increasing. This person is now gaining knowledge at a much faster rate than before.

In the meantime, what is happening with person A? There could be many reasons why the slope of the blue curve decreases, and this decrease simply indicates that knowledge, for this person, is now being gained at a slower rate than before. It is tempting to leap to the assumption that person A is now going to a “bad” school, with teachers who, at best, encourage rote memorization, rather than actual understanding of anything. Could this explain the change in slope? Yes, it could, but so could many other factors. It is undeniable that teachers have an influence on learning, but teacher quality (however it is determined, which is no easy task) is only one factor among many. Encouraging the “blame the teacher” game is not the goal of this model; there are already plenty of others doing that.

Perhaps person A became ill, suffered a high fever, and sustained brain damage as a result. Perhaps he or she is suddenly orphaned, therefore losing a previous, positive influence. There are many other possible factors which could explain this child’s sudden decrease of slope of the blue “learning curve” shown above; our species has shown a talent for inventing horrible things to do to, well, our species. Among the worst of the nightmare scenarios is that, while person B is learning things, at a distant school, the area where person A still lives is plunged into civil war, and/or a genocide-attempt is launched against the ethnic group which person A belongs to, as the result of nothing more than an accident of birth, and the bigotry of others. Later in life, on the graph above, the two curves intersect; beyond that point, person B knows more than person A, despite person B‘s slow start.  To give credit, or blame, to either of these people for this reversal would clearly be, at best, a severely incomplete approach.

At some point, of course, some people take the initiative to begin learning things on their own, becoming autodidacts, with high-slope learning curves. In other words, some people assume personal responsibility for their own learning. Most people do not. Few would be willing to pass such judgment on a child who is five or six years old, but what about a college student? What about a high school senior? What about children who have just turned thirteen years old? For that matter, what about someone my age, which is, as of this writing, 48? It seems that, the older a person is, the more likely we are to apply this “personal responsibility for learning” idea. Especially with adults, the human tendency to apply this idea to individuals may have beneficial results. That does not, however, guarantee that this idea is actually correct.

I must stop analyzing the graph above for now, because the best person for me to examine, at this point, in detail, is not on the graph above. He is, however the person I know better than anyone else: myself. I’ve been me now for over 48 years, and have been “doing math problems for fun” (as my blog’s header-cartoon puts it) for as long as I can remember. This is unusual, but, if I’m honest, I have to admit that there are inescapable and severe limits on the degree to which I can make a valid claim that I deserve credit for any of this. I did not select my parents, nor did I ask either of them to give me stacks of books about mathematics, as well as the mathematical sciences. They simply noticed that, when still young, I was curious about certain things, and provided me with resources I could use to start learning, early, at a rapid rate . . . and then I made this a habit, for, to me, learning is fun, if (and only if) the learning is in a field I find interesting. I had absolutely nothing to do with creating this situation. My parents had the money to buy those math books; not all children are as fortunate in this respect. Later still, I had the opportunity to attend an excellent high school, with an award-winning teacher of both chemistry and physics. To put it bluntly, I lucked out. As Sam Harris, the neuroscientist, has written, “You cannot make your own luck.”

At no point in my life have I managed to learn how to create my own luck, although I have certainly tried, so I have now reached the point where I must admit that, in this respect, Sam Harris is correct. For example, I am in college, again, working on a second master’s degree, but this would not be the case without many key factors simply falling into place. I didn’t create the Internet, and my coursework is being done on-line. I did not choose to be born in a nation with federal student loan programs, and such student loans are paying my tuition. I did not create the university I am attending, nor did I place professors there whose knowledge exceeds my own, regarding many things, thus creating a situation where I can learn from them. I did not choose to have Asperger’s Syndrome, especially not in a form which has given me many advantages, given that my “special interests” lie in mathematics and the mathematical sciences, which are the primary subjects I have taught, throughout my career as a high school teacher. The fact that I wish to be honest compels me to admit that I cannot take credit for any of this — not even the fact that I wish to be honest. I simply observed that lies create bad situations, especially when they are discovered, and so I began to try to avoid the negative consequences of lying, by breaking myself of that unhelpful habit. 

The best we can do, in my opinion, is try to figure out what is really going on in various situations, and discern which factors help people learn at a faster rate, then try to increase the number of people influenced by these helpful factors, rather than harmful ones. To return to the graph above, we will improve the quality of life, for everyone, if we can figure out ways to increase the slope of people’s learning-curves. That slope could be called the learning coefficient, and it is simply the degree to which a person’s knowledge is changing over time, at any given point along that person’s learning-curve. This learning coefficient can change for anyone, at any age, for numerous reasons, a few of which were already described above. Learning coefficients therefore vary from person to person, and also within each person, at different times in an individual’s lifetime. This frequently-heard term “lifelong learning” translates, on such graphs, to keeping learning coefficients high throughout our lives. The blue and red curves on the graph above change slope only early in life, but such changes can, of course, occur at other ages, as well.

It is helpful to understand what factors can affect learning coefficients. Such factors include people’s families, health, schools and teachers, curiosity, opportunities (or lack thereof), wealth and income, government laws and policies, war and/or peace, and, of course, luck, often in the form of accidents of birth. Genetic factors, also, will be placed on this list by many people. I am not comfortable with such DNA-based arguments, and am not including them on this list, for that reason, but I am also willing to admit that this may be an error on my part. This is, of course, a partial list; anyone reading this is welcome to suggest other possible factors, as comments on this post. 

Explaining China, Part II: What Do I Know, About China, and How Did I Learn It?

PRC and ROC and Barbarian Nations

In the map above, the People’s Republic of China (PRC) is shown in red, while the Republic of China (ROC) is shown in yellow. “Barbarian” nations (from the point of view of the Han, or the ethnic group we call “Chinese” in English) are shown in orange, and both oceans and large lakes are shown in blue. The third (and only other) majority-Han nation, the island city-state called Singapore, is not shown on this map, as it is too far to the South to be seen here. From the point of view of the Han, “barbarians” have been, historically, those humans who were not Han, while “the Han” can be translated as “the people.”

This historical xenophobia I just described among the Han is hardly unique; it is, in my opinion, simply human nature. The British rock band Pink Floyd explained this, quite well, in the following song, “Us and Them,” from 1973’s classic Dark Side of the Moon. This album, in the form of a cassette tape which had to be purchased by my parents (for I would not let go of it in the store we were in), happens to be the first musical album I actually owned, back when it was newly-released (I was born in 1968). If you choose to listen to this song, please consider this idea of xenophobia, as simply being a human characteristic, while it plays.

Ancient Greeks had the same “us and them” attitude about those who did not speak Greek, and the English word “barbarian” is derived from Greek, with a meaning which parallels what I have described in China. Eurocentrism, in general, in the study of “world history,” is well-known. Moving to another continent, the people where I live, the USA, are famous for learning geography one nation at a time . . . as we go to war with them, of course. Only a tiny percentage of Americans knew where either Korea was located until we went to war there, and we (as a people) did not know where Vietnam was until we went to war there. More recently, Americans learned — twice! — where Iraq is, though many of us still, inexplicably, confuse it with Iran. This list of xenophobic nations is far from complete, but these examples are sufficient to make the point.

When, in 1939, British Prime Minister Winston Churchill uttered the famous phrase, “It is a riddle, wrapped in a mystery, inside an enigma,” he was referring to the Soviet Union (or USSR), although the proper noun he actually used was “Russia.” However, this quotation applies equally well to the PRC, which has one indisputable advantage over the USSR: the People’s Republic of China still exists, while the Soviet Union does not. In the last post here, I began an ambitious series, with the goal of explaining China. I promised, then, that my next post in the series would explain my qualifications to write on the subject of the PRC, the ROC, Greater China, and the Han — so that’s what I need to do now.

I am currently working on my second master’s degree, in an unrelated field (gifted, talented, and creative education). However, my first master’s degree was obtained in 1996, when Deng Xiaoping, while no longer the PRC’s “paramount leader,” was still seen as its most prominent retired elder statesman. It was Deng Xiaoping, primarily, who made (and defended) the decision to send the tanks in, and crush the pro-democracy demonstrators in Tiananmen Square, in Beijing, in June of 1989, which I watched as they happened, on live TV. I was horrified by those events, and this has not changed.

During the early 1990s, I began studying the economic reforms which made the era of Deng Xiaoping so different from Chairman Mao’s China, trying to figure out the solution to a big puzzle: how so much economic growth could be coming from an area dominated by a huge, totalitarian, country which, at that time and now, was one of the few remaining nations on Earth which still claimed to be Communist. This study was done during the time of the “New Asia” investment bubble, as it was called after it “popped” (as all investment bubbles do, sooner or later). New Asia’s economic growth was led by the “Four Tigers” of Hong Kong (still a British colony, at that time), Singapore, Taiwan, and South Korea. South Korea is, of course, Korean, but the other three “tigers,” all had, and still have, majority-Han populations. What money I had, I invested in the Four Tigers, and I made significant profits doing so, which, in turn, led to a general interest in East Asia. 

Motivated by simple human avarice, I studied the Four Tigers intensely, leading me to focus (to the extent made possible by the course offerings) on 20th Century East Asian history, during the coursework for my first master’s degree. There was a problem with this, though, and I was unaware of it at the time. My university (a different one than the one I attend now) had only one East Asian history professor, and he was very much a Sinophile. Sinophiles love China uncritically, or with the minimal amount of criticism they can get away with. When we studied the rise to power of Mao Zedong, and the PRC under the thumb of Chairman Mao, I heard it explained by a man who viewed China, and Chairman Mao, through rose-colored glasses, even while teaching about others who made the same error, to an even greater degree. I had already read one book about the Cultural Revolution, earlier in the 1980s, so I was skeptical, but he was also my only professor. The result was confusion. This was the book I had already read, along with a link to a page on Amazon where you can purchase it, and easily find and purchase the Pink Floyd music posted earlier, if you wish to do so. This is Son of the Revolution, by Liang Heng and Judith Shapiro, and you can buy it at https://www.amazon.com/Son-Revolution-Liang-Heng/dp/0394722744/ref=sr_1_1?ie=UTF8&qid=1468869380&sr=8-1&keywords=son+of+the+revolution.

Son of the Revolution

This book was read for an undergraduate sociology course, at my first college, during the Reagan years. The important thing to know about Liang Heng, the book’s primary author, is that he was, himself, of the Han, as well as being from the PRC itself. The professor for this course wanted us to see the horror of a mass movement gone horribly wrong, and she chose this insider’s view of the Cultural Revolution, during which I was born, to do that. What I heard from my East Asian history professor did not mesh well with what I was taught by my East Asian history professor, and so I left that degree program confused. This professor’s argument, in a nutshell, was Chairman Mao was a figure of tremendous importance (true) who had good intentions (false), and tried to do amazing things (half-true, and half-false by omission, for these were amazing and horribly evil things), but had them turn out wrong (true), with many millions of his own people dying as a result, over and over (definitely true; Mao’s total death total exceeds that of Hitler or Stalin, either one). The “good intentions” part was what confused me, of course, for Mao was a monster, yet, from my later professor, I was hearing him described as a Great and Important Man.

I would have remained in this confused state, has I not also read this book, also written, primarily, by a person of the Han: the amazing Jung Chang, who has her own page on Amazon, at http://www.amazon.com/Jung-Chang/e/B00N3U50ZO/ref=sr_tc_2_0?qid=1468870698&sr=8-2-ent. (On that page, I notice she has a newer book out, which I have not read, and she is such a fantastic author that I am buying it now.) This, by contrast, was her first well-known book, and the one I read as an undergraduate:

wild swans

Wild Swans tells the story of three generations of Han women: Jung Chang’s maternal grandmother (who had bound feet, and could barely walk, for that reason), then the author’s mother, and then finally Jung Chang herself, who found herself a Red Guard during the Cultural Revolution at the age of 14. This book tells their story, and is riveting. It has nothing nice to say about Chairman Mao, and contains much criticism of “The Great Helmsman,” as his cult of personality enthusiastically called him, yet he is not the focus of Wild Swans. The author’s family, over three generations, is.

I did my master’s degree work from the Sinophile professor described earlier, and then, later on still, I encountered Sinophobes. The opposite of Sinophiles, people who have Sinophobia have nothing nice to say about China, nor the Han. They hate and fear things Chinese because they fear the unknown — in other words, Sinophobia is a more specific form of xenophobia. 

So, first, I read Liang Heng, and then, later, I started reading Jung Chang. Next, I heard the Maoist viewpoint explained quite thoroughly by my Sinophile professor, while my reading of Liang Heng and Jung Chang had exposed me to an anti-Mao, but non-Sinophobic, point of view, which is a direct consequence of the fact that both authors were actually of the Han, and had direct exposure to Maoism. Later came the Sinophobes, and their written and spoken, anti-Chinese, case for . . . whatever. (Actually, the Sinophobes never make a case for anything, unless one counts hating and fearing China and the Han as being “for” something. I do not.) Later still, one of my close friends studied ancient Chinese history and philosophy extensively, and we had (and still have) many talks about both ancient and modern China, including Chairman Mao, and the silliness of the Sinophobes, but this friend is more interested in talking about, say, Confucianism, rather than Maoism, or Mao himself. I was primed to learn the truth about Mao, but had to wait for the right opportunity.

Think about this, please. How many books have been written that accurately describe Stalin as a monster? How many exist about Hitler? I should not have had to wait so long to find out something about Mao I felt I could believe, and that described him as the monster he was, but wait I did, for no such book existed . . . until Jung Chang came to my rescue, with her next book, after 1991’s Wild Swans. All 800+ pages of it.

mao the unknown story

It took her many years to write this tome, and it was published in 2005. She grew up under Mao, having been born in 1952, not long after the revolution of 1949, which established the People’s Republic of China. Chairman Mao finally died in 1976. Two years after that, Jung Chang was sent to Great Britain as a college student, on a government scholarship. Being highly intelligent, and not wanting to return to China, she went on to become the first of the Han to receive a Ph.D. at any British university. This book, focused on Mao’s formative years, rise to power, and tyrannical rule, all the way to his death, is, as its subtitle states, “The Unknown Story” of this historical period. Jung Chang was uniquely qualified to write this story, having lived through so much of the events described in her book. She knew how expendable people were to Mao, having witnessed it, and survived. To the extent possible (and she was quite resourceful on this point) she used primary sources. This is why I give her much credibility. 

These are the ways I have learned about China: from three books by two of the Han, long talks with a personal friend, and two college professors with different points of view on China, and Mao in particular. I have rejected the points of view of both the Sinophiles and the Sinophobes, and now I try to learn what I can from other sources, especially sources who are, themselves, of the Han — although I am weakened in this respect by the fact that I am only bilingual, with my two languages being mathematics and English, in that order. If you think this approach makes sense, I hope you will read my other posts, past and future, about China and the Han.

How I Hit My Personal Mathematical Wall: Integral Calculus

Hitting the wall

To the best of my recollection, this is the first time I have written publicly on the subject of calculus. The fundamental reason for this, explained in detail below, is something I rarely experience: embarrassment.

Unless this is the first time you’ve read my blog, you already know I like mathematics. If you’re a regular follower, you know that I take this to certain extremes. My current conjecture is that my original motivation to learn how to speak, read, and write, before beginning formal schooling, was that I had a toddler-headful of mathematical ideas, no way to express them (yet), and learned to use English in order to change that. Once I could understand what others were saying, read what others had written, write things down, and speak in sentences, I noticed quickly that interaction with other people made it possible to bounce mathematical ideas around, using language — which helped me to develop and expand those mathematical ideas more quickly. Once I started talking about math, as anyone who knows me well can verify, I never learned how to shut up on the subject for longer than ten waking hours at a time.

A huge part of the appeal of mathematics was that I didn’t have to memorize anything to do it, or learn it. To me, it was simply one obvious concept at a time, with one exposure needed to “get it,” and remember it as an understood concept, rather than a memorized fact. (Those math teachers of mine who required lots of practice, over stuff I already knew, did not find me easy to deal with, for I hated being forced to do that unnecessary-for-me chore, and wasn’t shy about voicing that dislike to anyone and everyone within hearing range, regardless of the situation or setting. The worst of this, K-12, was long division, especially the third year in a row that efforts were made to “teach” me this procedure I had already learned, on one specific day, outside school, years earlier.) It might seem like I have memorized certain things, such as, say, the quadratic formula, but I never actually tried to — this formula just “stuck” in my mind, from doing lots of physics problems, of different types, which required it. Similarly, I learned the molar masses of many commonly-encountered elements by repeatedly using them to show students how to solve problems in chemistry, but at no time did I make a deliberate attempt to memorize any of them. If I don’t try to memorize something, but it ends up in memory anyway, that doesn’t count towards my extremely-low “I hate memorizing things” threshhold.

When I first studied calculus, this changed. Through repeated, forced exposure in A.P. Calculus class my senior year of high school, with a teacher I didn’t care for, I still learned a few things that stuck: how to find the derivative of a polynomial, the fact that a derivative gives you the slope a function, and the fact that its inverse function, integration, yields the area under the curve of a function. After I entered college, I then landed in Calculus I my freshman year. Unbeknownst to me, I was approaching a mental wall.

My college Cal I class met early in the morning, covered material I had already learned in high school, and was taught by an incomprehensible, but brilliant, Russian who was still learning English. Foreign languages were uninteresting to me then (due to the large amount of memorization required to learn them), and I very quickly devised a coping strategy for this. It involved attending class as infrequently as possible, but still earning the points needed for an “A,” by asking classmates when quizzes or tests had been announced, and only waking up for class on those mornings, to go collect the points needed for the grade I wanted.

This was in 1985-86, before attendance policies became common for college classes, and so this worked: I got my “A” for Cal I. “That was easy,” I thought, when I got my final grade, “so, on to the next class!”

I did a lot of stupid things my freshman year of college, as is typical for college freshmen around the world, ever since the invention of college. One of these stupid things was attempting to use the same approach to Calculus II, from another professor. About 60% of the way through that course, I found myself in a situation I was not used to: I realized I was failing the class.

Not wanting an “F,” I started to attend class, realizing I needed to do this in order to pass Cal II, which focuses on integral calculus. A test was coming up. In class, the professor handed out a sheet of integration formulas, and told us to memorize them.

Memorize them.

I read the sheet of integration formulas, hoping to find patterns that would let me learn them my way, rather than using brute-force memorization-by-drill. Since I had been skipping class, I saw no such patterns. All of a sudden, I realized I was in a new situation, for me: mathematics suddenly was not fun anymore. My “figure it out on the fly” method, which is based on understanding, rather than memorization, had stopped working.

A few weeks and a failed test later, I began to doubt I would pass, and tried to drop the class. This is how I learned of the existence of drop dates for college classes, but I learned it too late: I was already past the drop date.

I did not want an F, especially in a math class. Out of other options, I started drilling and memorizing, hated every minute of it, but did manage to bring my grade up — to the only “D” I have on any college transcript. Disgusted by this experience, I ended up dropping out of college, dropped back in later, dropped out again, re-dropped back in at a different university, and ended up changing my major to history, before finally completing my B.A. in “only” seven years. I didn’t take another math class until after attempting to do student teaching, post-graduation . . . in social studies, with my primary way of explaining anything being to reduce it to an equation, since equations make sense. This did not go well, so, while working on an M.A. (also in history) at a third college, I took lots of science and math classes, on the side, to add additional teaching-certification areas in subjects where using equations to explain things is far more appropriate, and effective. This required taking more classes full of stuff I already knew, such as College Algebra and Trigonometry, so I took them by correspondence (to avoid having to endure lectures over things I already knew), back in the days when this required the use of lots of postage stamps — but no memorization. To this day, I would rather pay for a hundred postage stamps than deliberately memorize something.

In case you’re wondering how a teacher can function like this, I will explain. Take, for example, the issue of knowing students’ names. Is this important? Yes! For teaching high school students, learning the names of every student is absolutely essential, as was quite evident from student teaching. However, I do this important task by learning something else about each student — how they prefer to learn, for example, or something they intensely like, or dislike — at which point memorization of the student’s name becomes automatic for me. It’s only conscious, deliberate memorization-by-drill that bothers me, not “auto-memorization,” also known as actually understanding something, or, in the case of any student, learning something about someone.

I don’t know exactly why my to-this-point “wall” in mathematics appeared before me at this point, but at least I know I am in good company. Archimedes knew nothing of integral calculus, nor did his contemporaries, for it took roughly two millennia longer before Isaac Newton and Gottfried Leibniz discovered this branch of mathematics, independently, at roughly the same time.

However, now, in my 21st year as a teacher, I have now hit another wall, and it’s in physics, another subject I find fascinating. Until I learn more calculus, I now realize I can’t learn much more physics . . . and I want to learn more physics, for the simple reason that it is the only way to understand the way the universe works, at a fundamental level — and, like all people, I am trapped in the universe for my entire life, so, naturally I want to understand it, to the extent that I can. (A mystery to me: why isn’t this true for everyone else? We’re all trapped here!) Therefore, I now have a new motivation to learn calculus. However, I want to do this with as much real understanding as possible, and as little deliberate memorization as possible, and that will require a different approach than my failed pre-20th-birthday attempt to learn calculus.

I think I need exactly one thing, to help me over this decades-old wall: a book I can read to help me teach myself calculus, but not a typical textbook. The typical mathematics textbook takes a drill-and-practice approach, and what I need is a book that, instead, will show me exactly how various calculus skills apply to physics, or, failing that, to geometry, my favorite branch of mathematics, by far. If any reader of this post knows of such a book, please leave its title and author in a comment. I’ll then buy the book, and take it from there.

One thing I do not know is the extent to which all of this is related to Asperger’s Syndrome, for I was in my 40s when I discovered I am an “Aspie,” and it is a subject I am still studying, along with the rest of the autism spectrum. One thing Aspies have in common is a strong tendency to develop what we, and those who study us, call “special interests,” such as my obsession with polyhedra, evident all over this blog. What Aspies do not share is the identity of these special interests. Poll a hundred random Aspies, and only a minority will have a strong interest in mathematics — the others have special interests in completely different fields. One thing we have in common, though, is that the way we think (and learn) is extremely different from the ways non-Aspies think and learn. The world’s Aspie-population is currently growing at a phenomenal rate, for reasons which have, so far, eluded explanation. The fact that this is a recent development explains why it remains, so far, an unsolved mystery. One of things which is known, however, is the fact that our status as a rapidly-growing population is making it more important, by the day, for these differences to be studied, and better understood, as quickly as the speed of research will allow, in at least two fields: medicine, and education.

Only one thing has fundamentally changed about me, regarding calculus, in nearly 30 years: I now want to get to the other side of this wall, which I now realize I created for myself, when I was much younger. I am also optimistic I will succeed, for nothing helps anyone learn anything more than actually wanting to learn it, no matter who the learner is, or what they are learning. In this one respect, I now realize, I am no different than anyone else, Aspie or non-Aspie. We are all, after all, human beings.

My New Middle Initial and Name: A Mathematical Welcome-Back Gift from My Alma Mater

UALR-Logo-1

I just had a middle initial assigned to me, and then later, with help, figured out what that initial stood for. With apologies for the length of this rambling story, here’s an explanation for how such crazy things happened.

I graduated from high school in 1985, and then graduated college, for the first time, with a B.A. (in history, of all things), in 1992. My alma mater is the University of Arkansas at Little Rock, or UALR, whose website at http://www.ualr.edu is the source for the logo at the center of the image above.

Later, I transferred to another university, became certified to teach several subjects other than history, got my first master’s degree from there (also in history) in 1996, and then quit seeking degrees, but still added certification areas and collected salary-boosting graduate hours, until 2005. In 2005, the last time I took a college class (also at UALR), I suddenly realized, in horror, that I’d been going to college, off and on, for twenty years. That, I immediately decided, was enough, and so I stopped — and stayed stopped, for the past ten years.

Now it’s 2015, and I’ve changed my mind about attending college — again. I’ve been admitted to a new graduate program, back at UALR, to seek a second master’s degree — one in a major (gifted and talented education) more appropriate for my career, teaching (primarily) mathematics, and the “hard” sciences, for the past twenty years. After a ten-year break from taking classes, I’ll be enrolled again in August.

As part of the process to get ready for this, UALR assigned an e-mail address to me, which they do, automatically, using an algorithm which uses a person’s first and middle initial, as well as the person’s legal last name. With me, this posed a problem, because I don’t have a middle name.

UALR has a solution for this: they assigned a middle initial to me, as part of my new e-mail address: “X.” Since I was not consulted about this, I didn’t have a clue what the “X” even stands for, and mentioned this fact on Facebook, where several of my friends suggested various new middle names I could use.

With thanks, also, to my friend John, who suggested it, I’m going with “Variable” for my new middle name — the name which is represented by the “X” in my new, full name.

I’ve even made this new middle initial part of my name, as displayed on Facebook. If that, plus the e-mail address I now have at UALR, plus this blog-post, don’t make this official, well, what possibly could?

“You Majored in WHAT?”

I’m in my twentieth year of teaching mostly science and mathematics, so it is understandable that most people are surprised to learn that I majored in, of all things, history.

It’s true. I focused on Western Europe, especially modern France, for my B.A., and post-WWII Greater China for my M.A. My pre-certification education classes, including student teaching, were taken between these two degree programs.

Student teaching in social studies did not go well, for the simple reason that I explain things by reducing them to equations. For some reason, this didn’t work so well in the humanities, so I took lots of science and math classes, and worked in a university physics department, while working on my history M.A. degree, so that I could job-hunt in earnest, a year later, able to teach physics and chemistry. As it ended up, I taught both my first year, along with geometry, physical science, and both 9th and 12th grade religion. Yes, six preps: for an annual salary of US$16,074.

History to mathematics? How does one make that leap? In my mind, this explains how:

  • History is actually the story of society over time, so it’s really sociology.
  • Sociology involves the analysis on groups of human minds in interaction. Therefore, sociology is actually psychology.
  • Psychology is the study of the mind, but the mind is the function of the brain, one of the organs of the human body. Psychology, therefore, is really biology.
  • Biological organisms are complex mixtures of interacting chemicals, and, for this reason, biology is actually chemistry.
  • Chemistry, of course, breaks down to the interactions of electrons and nuclei, governed by only a few physical laws. Chemistry, therefore, is really physics.
  • As anyone who has studied it knows, physics often involves more mathematics than mathematics itself.

…And that at least starts to explain how someone with two history degrees ended up with both a career, and an obsession, way over on the mathematical side of academia.

The Most Disturbing Thing I Ever Witnessed in a College Class

  • The Year: 1993
  • The College: The University of Central Arkansas
  • The Course: Educational Psychology

In a class called “Educational Psychology,” the bell curve, a statistical concept often used to describe the distribution of intelligence in humans, should be expected to receive some attention, and, when I took the class, it did — for about five minutes. I found the image below here; in this class, the professor drew a somewhat simpler version of it on a chalkboard.

Empirical_Rule (1)

The professor (who should be glad I do not remember his name, since I would blog it) proceeded to describe, briefly, characteristics associated with different “columns” of the bell curve, as some in academia apply it to intelligence. He then said, “Actually, what I’ve always really wanted to do was to get rid of these people.” He then added an “x” to what he’d drawn on the board. I’ve made it red, simply to make the location where he drew his “x” easier to see.

Empirical_Rule

I sat, in shocked silence, as the majority of the students in the class laughed. Laughed.

Once I could move again, after the initial, paralyzing shock turned into a deepening horror, I looked around the classroom. No one looked appalled, as I was; no one else even seemed to be disturbed, nor even slightly upset. Some were still visibly amused, in fact. I considered objecting, directly to the professor, but I was so affected by the whole episode that I was experiencing severe nausea. I couldn’t speak, for fear of throwing up.

The professor may not have known this — in fact, I would be surprised if he had — but what he was “joking” about has actually happened. It was called the Cambodian genocide, and was carried out by one of the most brutal regimes of the 20th Century, the Khmer Rouge. One of their tools used to stay in power was intimidation, taken to an extreme. In this photograph, from the article linked immediately above, you can see one form of this intimidation: the public display of the skulls of their victims. One need not be able to read to understand the message of such a display; below, the reason why this was important to the Khmer Rouge should become apparent.

800px-Choeungek2

I’ve studied this genocide. From just 1975 to 1979, the Khmer Rouge, driven by a radical Stalinist-Maoist and extremely anti-intellectual ideology, managed to reduce the population of Cambodia by an estimated 25%. They targeted, among many others, teachers. They separated children from their parents, since parents are often known to teach their children. They killed people who were seen wearing glasses — because glasses are often used to help people read books. They did their utmost to wipe out as much of the high-intelligence part of the bell curve as possible. They did their best to eliminate literacy.

Those who survived this horror were still devastated, for a whole nation had been traumatized — just imagine an entire country with PTSD (post-traumatic stress disorder). To make this situation even worse, the very people who could have helped most with the post-Khmer-Rouge recovery (doctors, therapists, teachers, clergy, etc. — all professions which require education) were almost entirely wiped out, and the people who could train new recruits for such professions had also been killed. As a direct result of this targeting of intellectuals for slaughter, the effects of the Cambodian genocide lasted far longer than the regime which perpetrated it.

I was thinking about this as the class period ended. In a daze, I walked away — far away. Even though I did return for future class sessions, since the course was a requirement for teacher certification, I never listened to another word that professor said, for he had permanently lost all credibility with me. At the end of the term, I left his class with an “A,” and a renewed determination to oppose those who, like the Khmer Rouge, try to “dumb down” society — at every opportunity. As for the people of Cambodia . . . they are still recovering, and will be, for many more years.

Wiping out a group of people — any group — simply isn’t funny.